Comedy and striptease: are they natural partners? We're not used to thinking of them as such, but Comic Strip, a show that combines striptease and burlesque on a late-night bill alongside standup, wants to change that. It might seem typical of the experimental spirit of the Fringe, but in fact the show is lovingly reviving an almost-forgotten tradition of underground entertainment. Burlesque, after all, takes its name from the Italian word "burla", meaning a joke.

My rare encounters with burlesque in the past haven't persuaded me it's an art form I want to devote much time to – I always feel an instinctive feminist unease about the idea of women taking their clothes off on stage. But I was intrigued by Comic Strip because it's the creation of Asher Treleaven, a comedian I've admired since his debut Fringe show last year, and his partner Gypsy Wood, a burlesque dancer who is also a self-taught historian of the form.

The show – which they insist is not variety but very specifically standup and striptease, with a changing bill of three comics, three dancers and a compere – is, they explain, an implicit tribute to Lenny Bruce and is intended as a celebration of free speech. Bruce was arrested a number of times in the 1960s and prosecuted for obscenity – on one occasion for using the word "schmuck" (a Yiddish word for penis) in his act. Undercover police would sit in the front row at his gigs, waiting for one word out of line; and it was only in the strip clubs, Wood explains, that Bruce was able to avoid the profanity laws and develop an act in which he was not afraid to talk about anything.

"So many comics now don't know about Lenny Bruce and that makes me sad," Wood says, "because he paved the way for all of them to say what they like on stage." Treleaven points out that much of what the comedians in the show talk about is far more explicit than what the dancers get up to, but it's this idea of striptease that seems to make good liberal Fringe audiences uncomfortable.

Perhaps one of the most striking things about Comic Strip is how much fun both performers and audience seem to be having, and how rare it is to see women who are not airbrushed, size-zero models enjoying their bodies and celebrating them. Neither is the audience in the Assembly's Dans Palais (a 1930s Spiegeltent) full of leering stag parties: it's overwhelmingly couples or groups of friends (and me, scribbling furiously in my notebook to justify sitting at the back by myself). I'm still not totally convinced it's my thing, but I like the idea that it's keeping an art form alive and celebrating the fact that live comedy no longer has to be afraid of censorship.